On vacuum polarization and plasma oscillations

Vacuum polarization in a strong electric field results in electron-positron pair creation. We study collective effects in the pair plasma emerged in this way, including vacuum polarization itself, back-reaction of the plasma on initial electric field and plasma oscillations. With this goal we consider energy conservation and electromagnetic field equations, comparing these to the traditional Vlasov-Boltzmann treatment. We conclude that under certain conditions plasma oscillations may occur in a weak electric field. We present single equation describing these oscillations in the weak field limit. Time and length scales of oscillations are discussed.